The Englishman started at the tip of the attack for the Gunners and provided the assist for Marquinhos to open the scoring on his debut just 16 minutes into the match.
Nketiah then went from hero to zero as he gave away a penalty at the end of the first half, which Mirlind Kryeziu dispatched to restore parity for Franco Foda's side.
However, the 23-year-old ended up netting the decisive goal at Kybunpark, as he met Marquinhos's cross and headed home at Yanick Brecher's near post just after the hour mark to propel the Gunners to a 2-1 win.
In doing so, Nketiah became just the fifth English player to score in three consecutive starts in the Europa League after also making the net ripple against Rapid Vienna and Dundalk in the 2020-21 group stage.
Harry Kane, Jermain Defoe, James Tavernier and Bobby Zamora are the only English players to have previously achieved the feat, and Nketiah now has 24 goals to boast from 99 outings in an Arsenal shirt.
Mikel Arteta's side will aim to make it two for two in Group A when they welcome PSV Eindhoven - who drew 1-1 with Bodo/Glimt on the opening day - to the Emirates next week.
The Gunners were due to take on Everton in the Premier League this weekend, but all top-flight, EFL and women's fixtures have now been postponed following the death of Queen Elizabeth II on Thursday.